During the operation of an internal combustion piston engine, gas and mass forces are produced per cylinder and, in the end, cause a resulting piston force. These resulting piston forces, in their turn, overlap each other differently depending on the number and arrangement of the cylinders along the crankshaft of the internal combustion engine and, depending on the manner of overlap, they cause free forces and torques. These free forces and torques add to the loading of the engine supports, reduce comfort and produce noises. For this reason, compensation shafts are increasingly used in present-day internal combustion engines in which free forces and torques occur. These compensation shafts comprise weight sections that cause controlled states of imbalance to compensate the free forces and torques. For this purpose, the compensation shafts are operated at the same speed of rotation or at double the speed of rotation of the crankshaft, depending on whether forces or torques of the first or the second order have to be compensated for. Thus, it is possible in this way to improve the smoothness of running of a multi-cylinder engine.